The former Tottenham and Aston Villa winger joins Brendan Rodgers' newly promoted side for an undisclosed fee, becoming the second signing in two days at the Liberty Stadium
Routledge becomes manager Brendan Rodgers’ second signing in as many days after Leroy Lita arrived from Middlesbrough.
“I'm looking forward to the challenge,” Routledge told the club’s official website.
“It's taken a couple of days to get everything agreed, but I'm excited about getting started.
“I've had a good chat with the manager and he really impressed me.
“I had heard a lot of good things about him and the chat only reinforced my belief that moving to Swansea was the right thing to do.”
The 26-year-old, who will wear the No.15 shirt at the Liberty Stadium, becomes the Swans’ fifth signing of the summer.
And Routledge is pleased to be joining a team who earned praise last year for their playing style.
“Having watched Swansea last season, I think everyone would agree that they were the best footballing side in the Championship,” said the winger.
“It's going to be a difficult first season in the Premier League; it's going to be tough.
“But everyone is confident and looking forward to it. After all, playing in the Premier League is what you dream of. I'm excited about it.”
Routledge could make his first appearance in a Swansea shirt in a friendly against Real Betis on Saturday.